Not being bounded to conjugacy allows us first to use any relevant kernel for the mixture.
Moreover, even in the case of the normal kernel, this removes the dependence imposed in the conjugate case between the location of the clusters and their variances.
More precisely, this allows a full flexibility on specifying priors based on external knowledge, and proves particularly useful concerning the scale parameters of the kernels.
Indeed, half-Cauchy or half-Gaussian priors for hierarchical variance parameters have recently become popular [1]}, [2]}.
The illustration on ssd (sec:casestudy), where the data is scaled, offers such an example where both an upper bound and lower bound on the cluster variances are useful.
